Forty-three missing students abducted by corrupt police in south-west Mexico six weeks ago were apparently incinerated by drug gang henchmen and their remains tipped in a garbage dump and a river, the government says.

Attorney-general Jesus Murillo said three detainees, caught a week ago, admitted setting fire to a group of bodies in a dump near Iguala in the state of Guerrero, where the trainee teachers went missing on September 26 after clashing with local police.

Then the perpetrators set about removing all the evidence, Mr Murillo told a news conference, showing taped confessions of the detained, photographs of where remains were found and video re-enactments of how the bodies were moved.

"They didn't just burn the bodies with their clothes, they also burned the clothes of those who participated," Mr Murillo said, adding the gang members spent over 12 hours torching the remains.

"They tried to erase every possible trace."

The government said police working with a local drug gang abducted the students after the clashes.

The kidnapping triggered mass protests in much of the country and seriously undermined president Enrique Pena Nieto's claims that Mexico has become safer on his watch.

The disappearances have been the toughest challenge yet to face Mr Pena Nieto, who took office two years ago vowing to restore order in Mexico, where about 100,000 people have died in violence linked to organised crime since 2007.

Mr Pena Nieto said the findings had "shocked and offended" Mexico and pledged to round up everyone involved.

As long as there is no proof, our children are alive.

Felipe de la Cruz, father of missing student

"The investigations will be carried out to the full, all those responsible will be punished under the law," he said.

Dozens of police are among 74 people held in the case.

The scandal has forced Mr Pena Nieto to cut short a planned visit to China next week, and angry relatives of the missing students said the government had only made the announcement to clear the path for the president to go.

"Pena Nieto should think hard about his trip," said Felipe de la Cruz, father of one of the missing students.

"As long as there is no proof, our children are alive."

The confessions of the gang members pointed to the murder "of a large number of people," Mr Murillo said, showing a video of one suspect saying the victims had said they were students.

Identifying the remains, which were ground up after burning, was so difficult that it was impossible to say when final results would come in, Mr Murillo said.

But he said there was much evidence "that could indicate it is [the students]".

Teeth of victims found at the scene were so badly burned that they virtually turned to dust upon contact, Mr Murillo said, adding that the remains would be sent to the University of Innsbruck in Austria for final DNA identification.

The government would continue to view the students as missing until their identities are confirmed, he added.

Testimony from investigators suggested that the students, from an all-male leftist college, had clashed with the mayor in the past and that the city police had handed them over to local gangsters who killed them.

The case has dented Mr Pena Nieto's popularity and derailed his efforts to turn public attention toward a string of reforms he passed in the first part of his government, which he hopes will spur stronger growth in Mexico's misfiring economy.